Mapping a deep Gaussian process

Best viewed in HD. The colors show the location that each point in a grid is mapped to, after being mapped through a random smooth function drawn from a deep Gaussian process prior.
The mapping starts without any distortion, then each layer is successively added to the mapping. By the end, there are 50 layers of warpings.

[@ish694]

So if we had used a single standard GP, the mappings would have stopped at the 1st change/mapping itself right ?

[@tookerjerbs]

Yes, the first mapping is just a function drawn from a single standard GP.

[@nathangold573]

This is very beautiful. How did you produce these images?

[@tookerjerbs]

Thanks! The code to produce these images is here:
github.com/duvenaud/deep-limits/blob/master/source/deep_color_map_video.m
As for what the colours mean, they are just a color-coding of the representation computed at each input location. The representation changes as more layers are added to the computation.

[@ish694]

So if we had used a single standard GP, the mappings would have stopped at the 1st change/mapping itself right ?